What is (\partial)/(\partial x)(x(1-x-2y)) ?

The answer to (\partial)/(\partial x)(x(1-x-2y)) is -2x-2y+1

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(\partial)/(\partial x)(x(1-x-2y))

\frac{\partial}{\partial x} (x (1 - x - 2 y))

- 2 x - 2 y + 1

Solution steps

\frac{\partial}{\partial x} (x (1 - x - 2 y))

Treat

y

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = 1 - x - 2 y

= \frac{\partial}{\partial x} (x) (1 - x - 2 y) + \frac{\partial}{\partial x} (1 - x - 2 y) x

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (1 - x - 2 y) = - 1

= 1 \cdot (1 - x - 2 y) + (- 1) x

Simplify

1 \cdot (1 - x - 2 y) + (- 1) x : - 2 x - 2 y + 1

= - 2 x - 2 y + 1

y^{'} = 0.002 y (2500 - y)

\frac{d ^{2}}{d x ^{2}} (x^{3} + y^{3})

π^{2}

\int \frac{2}{3 x - 2} d x

\frac{d}{d x} ((sec (2 x))^{7})

What is (\partial)/(\partial x)(x(1-x-2y)) ?
The answer to (\partial)/(\partial x)(x(1-x-2y)) is -2x-2y+1